Magyar
Kem. Folyoirat 66, 250-1 (1960). (124) Schulek, E., Maros, L., Acta Chim. Acad. Sci. Hung. 19,473-8 (1959). (125) Ibid.. 20. 443-9 (1959). (126) Schulek,’ E., Maros,‘ L., Magyar Kem. Folyoirat 64, 480-2 (1958). (127) Scott, R. L., Puckett, J. E., Price,
H. A., Grimes, M. D., Henrich, B. J.,‘ Ana1:Chim. Acta 23, 428-33 (1960). (128) Semin’ko, V. A,,, Trudy Khar’kov. Farm. Inst. 1957, No. 1, 158-9. (129) Sietz, F. G., Chemiker-Ztg.84,362-4
(1960). (130) -Siggia, S., Hanna, J. G., Culmo, R., k A L . CHEM. 33, 90Q-1 (1961). (131) Singh, B., Sahota, S. S., Singh, R. P.. J . Indian Chem. SOC.37, 392-4 (1960). (132) Slusanschi, H., 2. Lebensm. -7Jntersuch. u.- Forsch. 112, 390-1 (1960). (133) Smith, J. C. V., Analyst 85, 465-74 (1960). (134) Stephen, W. I., Proc. Intern. Sym-
posium Microchem., Birmingham Univ.
1958, 163-7 (Pub. 1959). (135) Sully, D. D., Analyst 85,895-7( 1960). (136) Sundbern. 0. E.. Maresh. C.. ASAL. ‘ CHEM.32. 2y4-7 (1’960). ’ ’ (137) Takigbchi, T., ‘KogybKagaku Zasshi 61, 587-8 (1958). (138) Terent’ev, A. P., Buzlanova, M.
M., Obtemperanskaya, S. I., Zhur. Anal. Khim. 14, 506 (1959). (139) Toth, Z., Krasznai, I., Magyar Kem. Folyoirat 65, 289-91 (1959).
(140) Tuckerman, M. M., Hodecker, J.
H., Southworth, B. C., Fleischer, K. D., Anal. Chim.Acta 21, 463-7 (1959). (141) Vanderzee, C. E., Edgell, W. F.,
ANAL.CHEM.22, 572 (1950). (142) VeEefa. M.. Acta Chim. Acad. Sci. . Hung. 26, 511-18 (1961). (143) VeEefa, M., Synek, L., Collection Czechoslov. Chem. Comntuns. 24, 3402-6 (1959). (144) Veibel, S., Chem. Zisty 54, 820-33 (1960).
(148) Veibel, S., Proc. Intern. Symposium Microchem., Birmingham Univ. 1958, 159-62 (Pub. 1959). (146) Vitovec, J., Sadek, M., Collection Czechoslov. Chem. Communs. 25, 1972-4 (1960). (147) Vogel, A. M., Quattrone, J. J., Jr., ANAL.CHEM.32, 1754-7 (1960). (148) Voronkov, M. G., Shemyatenkova,
V. T., Izvest. Akad. Nauk S.S.S.R., Otdel Khim. Nauk 1961, 178-80.
(149) Walisch,
W.,Hertel, D. F., Ashworth, M. R. F., Chem. anal. 43, 234-7
(1961). (150) Whitman, C. L., Roecker, G.
W.,
McNerney, C. F., ANAL. CHEY. 33,
781-2 (1961). (151) Wolf,. F.., 2. anal. Chem. 172,413-23 (1960). (152) Wrdnski, M., ANAL. CHEM. 32, 133-4 (1960). (153) Wr6nski, M.,2. anal. Chem. 174, 3-5 (1960). (154) Ibid., pp. 280-1. ’
Review of Fundamental Developments in Analysis
X-Ray Diffraction, Crystal Structure Analysis, and the- High-speed Computer G. A. Jeffrey and M a r t i n Sax, The Crystallography laboratory, The University of Pittsburgh, Pittsburgh 13, Pa.
T
analysis of the structure of matter by x-ray diffraction is an interdisciplinary technique which has applications in chemistry, biochemistry, biophysics, solid-state physics, geology, ceramics, mineralogy, and metallurgy (56). I n fact, in its emphasis on the basic structure of materials it tends to make the barriers between these sciences appear somewhat superficial. This was well illustrated by the range of topics covered by the 600 papers presented a t the Fifth Congress of the International Union of Crystallography (34), many of which were concerned with the use or results of x-ray diffraction methods. As with most techniques having such a broad application, it often happens that a cross fertilization of concepts occurs between rather distant sciences because of a common interest in the experimental method. As a pure technique, x-ray diffraction analysis requires a good knowledge of elementary physics and, in these days particularly, a sufficient grasp of applied mathematics to be able to harness to one’s requirements the facilities of the high speed computer. Nevertheless the real incentives for the investigation usually come from the scientific area where the results are fully understood and their significance is most appreciated. Hence the aphorism pertaining to crystal structural analysis HE
that only the physicist knows how to do it, but only the chemist knows why. For the more chemically oriented scientist interested in the atomic structure of materials, x-ray diffraction technique has a variety of applications, the more important of which can be classified as follows : Study of order in liquids and noncrystalline or partially crystalline solids Identification of single crystalline phases Quantitative measurement of certain chemical and physical data, such as density, molecular weight, stoichiometry, polymorphism, hydration, or solvation in crystals Determination of crystal structures. The majority of these investigations have as their objective the elucidation of an unknown chemical configuration or the study of the nature of the intraor intermolecular binding forces. Phase transformations can be studied by determining the structures on either side of the transitions and this has been applied mainly to ferroelectrics (81),orderdisorder in alloys (40), and molecular structures involving the onset of orientational or rotational disorder (66). The idea of following a solid-state reaction by observing the structural changes by means of the diffraction pattern of a single crystal is an attractive one, but instances where this might be possible are rare (22, 27, 37, 86).
With varying emphasis, these topics have been periodically reviewed in the previous articles in this series (30, 46-45, 779, together with some provocative remarks on the training of chemical crystallographers. The present review covers the period from 1958 to 1961. As regards the fundamental methods involved, there is not much to add to what has previously been said. The already comprehensive literature on xray diffraction methods has been brought up to date by new books (11,12, dl,56,67, 73, 85,88,85). The characteristic of the development in x-ray diffraction analysis during the period of this review has been an increase in complexity and specialization in the methods of interpretation and an improvement of existing experimental techniques and of the commercially A world-wide available equipment. index of crystallographic supplies was produced in 1959 (83), and another edition is planned for 1963. The increased sensitivity and convenience of the proportional and scintillation counter detectors over photographic film for recording x-ray diffraction spectra have been exploited for powder diffraction methods, but the revolution in single-crystal techniques has developed much more slowly. The most important technical development has been the effect of the high-speed comVOL. 34, NO. 5, APRIL 1962
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puter on the interpretative aspects of the methods. NONCRYSTALLINE OR PARTIALLY CRYSTALLINE MATERIALS
The determination of the structural parameters in noncrystalline substances by x-ray diffraction has made some important contributions in the field of coal research (14, 26, 28). A new least-squares method for the analysis of the diffuse scattering from noncrystalline substances has been described (25) and has been successfully applied to polymers containing small aromatic ring systems ( 7 9 ) . The type of parameters used in this method were amorphous content, aromatic size distribution, mean layer size, and mean bond length. The exciting developments in the field of polymer chemistry arising out of the discovery of the Ziegler-type catalysts a fen. years ago stimulated much activity in the use of x-ray diffraction, since the new isotactic polymers tended t o be more crystalline than the older synthetic polymers. X-ray methods were used both for identifying phases (60, 60, 6W,64) and for measuring the crystalline-amorphous ratio (32, 33,45, 63). The preferred orientation of densely packed linear polymer molecules has been analyzed in terms of bundles of parallel line scatterers (3, 68). Lowangle scattering has been used for studying crystallization (69) and there have been some interesting examples of the use of s-ray diffraction in conjunction Tvith infrared spectroscopy and (42) nuclear magnetic resonance (31, 65). However, from the point of view of making fundamentally new discoveries concerning the structure of the polymer molecules in the crystalline state, it would appear, a t present, that the application of selected area and dark field electron microscopy combined with electron diffraction of polymer single crystals and spherulites is the more promising technique. Similar technical and interpretative problems are experienced in the application of x-ray diffraction to exploring the degree and nature of the structural order in natural polymeric materials. The burst of activity which followed the discovery of the helical transform method (15) has somewhat abated, although this method is still being effectively exploited (20, 36, 75, 82). The Symposium on the Microstructure of Proteins a t the September 1960 meeting of the American Chemical Society was dominated by the discussion of the single-crystal diffraction studies of Kendrew and Perutz. There have been comparatively fen7 applications to the study of liquids (8, 3, 6 5 ) . This method has become in340 R
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creasingly effective over the past ten years because of the improvement in instrumental technique and seems now to be capable of wider application to chemical problems. IDENTIFICATION OF CRYSTALLINE MATERIALS AND MEASUREMENT OF CHEMICAL AND PHYSICAL DATA
Identification by means of the x-ray powder diffraction pattern is a long established technique to which there have been no major improvements during the period of this review. The ASTM X-ray Powder Data File nom goes to set 11 and the index and sets 1 to 5 are also available in book form (4). The usefulness of these data is continually being improved by both the accession of nelT data and the revision of old data through the publication of “Comments on the ASTM Powder Data File,” Sos. 1 to 6 (43). Two new books on the powder diffraction method have been published (6,2.4). In the 1958 review, an important question of policy was asked in regard to the inclusion of organic compounds, with a potential membership of 1,000,000, in the Powder Data File. A big influx of data relating t o organic compounds might seriously impair the present usefulness of the file for inorganic materials, unless some special provision was made. After set 7 , the file is now separated into inorganic and organic sections. The appearance of special publications or papers pertaining to particular classes of materials may also provide a temporary answer to this problem (71). In the study of natural products, where the organic chemical data file is likely to be most useful, identification is often required within a limited class of compounds rather than as a completely unknown substance. Eventually, the magnitude of this problem mill become such that it must be tackled by the application of modern information-retrieval methods using the electronic data-processing machines, and perhaps some thought should already be given to the storage and retrieval of these data using magnetic tape. The relationship lid = 1.6606 nM, where V is the volume of the crystal unit cell, in cubic Angstroms, containing n molecules of molecular weight JI and d is the density, provides a very useful method for the measurement of molecular weights and for studying stoichiometry, hydration, etc. (68), and it is surprising that more use is not made of it in chemical laboratories. As a means of studying crystal texture, imperfections, and dislocations, the method of x-ray diffraction microradiography (53) has been very successfully developed and applied. The comparison of thermal expansion coefficients by x-ray and dilatometric measurements
has given conflicting results, which are interpreted as due in part to crystal defects (23,64). An international project for the comparison of precision lattice parameter measurements on identical samples gave agreement of 1 part in 104, which is an order of magnitude greater than the precision often claimed by individual investigators (70). CRYSTAL STRUCTURE ANALYSIS AND HIGH-SPEED COMPUTER
In the application of x-ray diffraction
to the determination of atomic and electronic structure of molecules in crystals, the last four years have been a period of extraordinarily rapid development in the use of high-speed digital computers. These instruments now play a dominant role in crystal structure analysis, and the progress toward full automation of the method has been such as to suggest that this may be achieved within the next decade. For better or worse, the crystal structure analyst dreams of a nirvana where a machine takes the crystal, records the data, analyzes them, and prints out the ansvers he requires. The development of such an instrument to record, automatically or even semiautomatically, the x-ray diffraction data from single crystals and interpret them in terms of atomic structure could bring about a profound change, not only in the science of crystallography, but in other sciences where structure plays an important role. The association between x-ray crystallography and computing was, in fact, predicted in 1915 by W. H. Bragg, when the science was only three years old. Bragg gave the first presentation of the equation for the application of Fourier’s theorem to the calculation of the electron density distribution in a crystalline material. However, a t that time and for some 20 years after, this equation was much like Schroedinger’s wave equation in quantum mechanics; therein lay the answer to many problems, but the application led to calculations much too complicated to be soluble. It was not until the late 1930’s that attempts were made to carry out the laborious computations of the Fourier synthesis on specially designed relay or analog computers. These mere primitive contraptions compared with the modern computer. However, enough results were obtained Kith these machines, and their more successful successors, such as X-RXC (74), and with ordinary desk computers and business tabulators (17, 80) to reveal the necessity for a closer examination of the mathematical methods whereby x-ray diffraction data were interpreted in terms of the details of molecular structure. This phase of development
was essentially completed about ten years ago, when the first of the modern high-speed computers began t o make their appearance. The crystal structure analyst was therefore ready, with his equations and computational procedures well thought out ahead of the development of the necessary computing hardware (2, 7 , 44). It was not surprising, therefore, that progress was fast, once the computing facilities were sufficiently widespread to be generally available and the necessary programs had been written. The latest computer program listing of the American Crystallographic Xssociation records 350 programs for the dozen or so computers commonly available in this country. In nearly all cases these programs were ritten by ci >-stallographers; for apparently it i b easier for a crystallographer t o learn computer machine language than for a programmer to learn crystal structure analysis, and thcre was thc excitement of a nen- power to provide the incentives. X similar World List of Crystallographic Computing programs is being assembled by a commission of the International Union of Crystallography ( 1 ) . It is reasonable to assume that every commercial high-speed computer is by now completely programmed for the more routine computations of crystal structure analysis or N ill be n ithin 12 months of its initial appearance in a major university. The status of crystallographic computing up to mid-1960 is reviewed in a conference report (76). The effect of computers on crystal structure analysis has been twofold: t o decrease substantially the time spent on completing the problem and to increase the range of problems which can be tackled with a rmsonable hope of success. At the 1960 Congress of Crystallography ( 3 4 , one paper reported five organic structure analyses of about tenatom complexity (excluding hydrogen), one of which (catechol) was completed in about three weeks. I s was pointed out in a reviex of this meeting (87)), three weeks was also about the time required to build the model which was necessary to present the detailed results of the most complex structure analysis reported, that of the 153-amino-acid protein, sperm-whale myoglobin. With a desk calculator the catechol structure analysis might have been completed in two years and analyses of the protein str ucture would have been completely impossible. The reduction in the time required for the completion of a structure analysis has resulted in a corresponding increase in the number of analyses published and in the precision and detail in the results. Many of these publications are to be found in one of the three crystallography iournals: Acta Crystallographica, Zeit-
schrift fur Kristallographie, and Crystallography (84). Even so it is often
difficult, even for the crystallographer, to discover whether a particular compound has been subjected to a structure analysis within the past few years. Unfortunately, the standard reference, “Structure Reports,” Volumes 8 to 16, is still ten years behind and does not show much sign of catching up with the rapidly increasing amount of published structural data. A new edition of the 1958 “Tables of Interatomic Distances and Configuration in RIolecules and Ions” is promised but has not yet appeared. In this field, as in many others, the problem of information retrieval is becoming increasingly difficult. An International Conference on Scientific Information in the Field of Crystallography and Solid State Physics was held a t Kwansei Gakuin University, Japan, in October 1961. The best comprehensive review covering 19591960 is to be found in the crystallography section of the 1960 “Annual Reports on the Progress of Chemistry” (16). These structural studies have ranged from the elemental substances, diamond and silicon (10, 38, SQ), to the most coniplex crystals, the crystalline proteins (51, 76). I n the very simple compounds, the objectives have been to study the distribution of the valence bond electrons (61) or make measurements relating to the nature of the chemical bonding. There have been very many investigations of intermetallic compounds, and a supplement to the “Handbook of Lattice Spacings and Structures of Metals and Alloys” (72) would be most useful. A large number of medium-sized inorganic and organic structures have been investigated for the determination of coordination and stereochemistry and the measurement of bond lengths. I n some of the organic molecular structures not only have the positional parameters of the atoms been determined but also their thermal parameters. This has permitted, in favorable cases, a complete analysis of the thermal motion in terms of a rigidbody molecular motion following the methods of Cruickshank (18). A number of organic structures of natural products have been determined where the chemical configuration of the molecule was unknown, particularly by Robertson and coworkers (78). Undoubtedly the most spectacular achievement in structure analysis during the period of this review is the work on the crystalline proteins, myoglobin and hemoglobin. In comparison, one would think that the problems a t the other extreme, involving the very precise determination of a few parameters, would be simple. In fact, a considerable effort has been put into attempts to determine the three posi-
tional parameters of the tetragonal form of barium titanate with sufficient accuracy to contribute to a better understanding of the nature of the ferroelectric transition. It would now appear that despite some very careful experimental measurements and an excellent ratio of observations to unknown parameters, the problem is essentially indeterminate. This disturbing result arises from the interactions between certain positional and thermal parameters in the least-squares matrix (29). I t may impose serious limitations to precision analyses of structures with polar axes and high symmetry. Methods of overcoming this difficulty are not yet apparent, but, a t least, a technique for recognizing and perhaps anticipating them has been suggested (S6). The increase in speed of the interpretative stage of the structure analysis has turned attention to the collection of the experimental data, which now can sometimes be the slowest stage in the research. The requirements in terms of number of data and the precision of the measurements for a desired accuracy to 1 0 . 0 1 A. in interatomic distances has been estimated quantitatively (19). Such analysis would permit a comparison betaeen the results of molecular orbital and valence bond theories in aromatic hydrocarbons and would make the accuracy of the x-ray analyses of medium-sized molecules comparable with that of electron diffraction and spectroscopic methods for small molecules. For many years the experimental procedure commonly used for the recording and measurement of the diffraction data was a “time-honored” photographic method practically unchanged since the 1930’s. The successive development of the Geiger, proportional, and scintillation counters for x-ray recording from 1950 onward did not revolutionize the experimental aspects of crystal structure analysis quite as dramatically as was originally anticipated. This was because the commercially available diffractometers were primarily designed for powder identification and lattice dimension studies and were not easily adapted for single-crystal work. Xew auxiliary equipment (41) or specially constructed single-crystal diffractometers, with much higher standards of instrumentation, m-ere necessary. The appearance in 1960 of the first fully automatic single-crystal instrument with the input and output on high-speed computer tape was, therefore, an exciting event ( 5 ) . This piece of equipment, which is now commercially available, was especially designed for dealing with the vast amount of observational data required in protein crystal studies and may not be the ideal instrument for general strucVOL. 34, KO. 5 , APRIL 1962
341 R
ture analysis. Nevertheless, it represented a n important break-through in instrumental technique which should stimulate manufacturers in this country to try to follow the European lead. Between the automation of the measurement of the experimental data and the automation of the interpretative procedures known as the structure refinement on the high-speed computer lies the “phase problem.” This is the hard core of the crystal structure analysis technique, because although there are many methods for determining the phase of the structure factors, the amplitudes of which are measured experimentally, there is, as yet, no one method or combination of methods which is guaranteed to succeed. Here again the computer has helped to solve the problem both by making it possible to try several methods in a reasonable period of time and by leading to the development of new methods which would be quite impossible without the computer. The status of the art of solving crystal structure analyses has recently been evaluated (76) and certain aspects of this problem are discussed in a more unified manner by Woolfson (90)*
There are five stages in a crystal structure analysis, which, when individually automated and the whole integrated into a system with a highspeed computer of appropriate speed and capacity, constitute a n instrument for crystal structure analysis. 1. Measurement of the x-ray diffraction intensities 2. Reduction of intensities to structure amplitudes 3. Solution of the phase problem 4. Refinement of the structure 5 . Presentation of the final results in terms of stereochemical information
The present situation is that several instruments for stage 1 have been described and one of these is in commercial production; stages 2, 4, and 5 are routine procedures for most problems on a variety of computers. An interesting example of the display of the results of a structure analysis as a stereoscopic picture on a cathode-ray tube has been described ( I S ) . There is no doubt that the vital stage, 3, can be programmed for certain types of problems, but it is yet to be demonstrated that a universally applicable crystal structure solving instrument is possible. LITERATURE CITED
(1) Acta Cryst. 14, 898 (1961).
(2) Ahmed, F. R., Cruickshank, D. W. J., Zbid., 6, 765 (1953). (3) Alexander. L. E.. Michalik. E. R.. ‘ Ibid., 12, 105 (1959). (4) Am. SOC. Testing Materials, 1916 Race St., Philadelphia 3, Pa., “ASTM
X-Ray Powder Data File.”
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(5) Amdt, V. W., Phillips, D. C., Acta Cryst. 14,807 (1961). (6) Asaroff, L., Buerger, M. J., “ThePow-
der Method in X-Ray Crystallography,” McGraw-Hill, New York, 1958. (7) Bennett, J. M., Kendrew, J. C.,
Acta Cryst. 5, 109 (1952). (8) Brady, G. W.,J . Chem. Phys. 29, 1371 (1958). (9) Brady, G. W., Petz, J. I., Zbid., 34, 332 (1961). (IO) Brill, R., Zandy, H., Nature 183,1387 (1959). (11) Buerger, M. J., “Crystal Structure Analysis,” Wiley, New York, 1960. (12) Buerger, M. J., “Vector Space and
Its Application in Crystal Structure Investigation,” Wiley, New York, 1959. (13) Busing, W., American Crystallographic Association meeting, Abstracts, January 1960. (14) Cartz, L., Hirsch, P. B., Phil. Trans. Roy. SOC.London 252, 557 (1960). (15) Cochran, W., Crick, F. H. C., Vand, V., Acta Cryst. 5 , 581 (1952). (16) Cochran, W., Sutor, D. T., Green,
D. W.,“Annual Re orts on the Progress of Chemistry,” Cl?em. Soc., London,
1960. (17) Cox, E. G., Jeffrey, G. A., Acta Crust. 2. 341 (19499). (18) uCrui&kshank,D. W. J., Zbid., 9, 747, 754 (1956). (19) Ibid., 13, 774 (1960). (20) Davies, D. R., Rich, A., Zbid., 12, 97 (1959). (21) de J o y , W. F., “General Crystal-
lography, Freeman, San Francisco, Calif.. 1959. (22) Dent Glasser, L. S., Glasser, F. P.,
Acta Cryst. 14, 818 (1961). (23) Desphande, V. T., Mudholder, V. M., Zbid., 13, 483 (1960). (24) D’Eye, R. W. M., Wait, E., “X-Ray
Powder Photography in Inorganic Chemistry,” Butterworths, London,
1960. (25) Diamond, R., Acta Cryst. 11, 129 (1958). (26) Diamond, R., Phil. Trans. Roy. SOC. London 252, 193 (1960). (27) Donnay, G., Wyart, J., Sabatier, G., 2. Krist. 112, 161 (1960). (28) Ergun, S., Tiensui, W. H., Acta Cryst. 12, 1050 (1959). (29) Evans, H. T., Ibid., 14, 1019 (1961). (30) Fankuchen, I., ANAL. CHEM.30, 593 (1958). (31) Farrow, G., Brit. J . A p p l . Phys. 11, 543 (1960). (32) Farrow, G., Preston, D., Ibid., 11, 353 (1960). (33) Farrow, G., Ward, I. M., Zbid., 11, 534 (1960). (34) Fifth Congress Intern. Union Crystallography, Acta Cryst. 13, 965-1164 (1960). (35) Fraser, R. D. B., MacRae, T. P., Nature 189, 572 (1961). (36) Geller, S., Acta Cryst. 14,1026 (1961). (37) Gillespie, R. B., Sparks, R. -4., Trueblood, K. N., Zbid., 12, 867 (1959). (38) Gottlicher, S. von, Kuphal, R.,
Sagorsen, G., Woelfel, E., 2. phys.
Chem. 21, 133 (1959). (39) Gottlicher, S. von, Woelfel, E., 2. Elektrochem. 63, 891 (1959). (40) Guttman., L.., Solid State Phus. 3. 1
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145(1956). (41) Harker, D., Furnas, T. C., Rev. Sci. Znstr. 26,449 (1955). (42) Hendus, H., Schnell, G., Kunststoje 51, 69 (1961). (43) Hughes, J. W., Lewis, I. E., Wilson, A. J. C., Brit. J . A p p l . Phys. 11,306 (1960). (44) Jeffrey, G. A,, Cruickshank, D. TV. J., Quart. Rev. Chem. SOC.London 7, 335 (1953). 145) Kadudo, M., Ullman, R., J . Polymer
OxTord, 1961. (68) Ohlberg, S.,
’
Alexander, L. E., Warrick, E., J . Polymer Sci. 27, 1
f1958). --,(69) Onions, W. J., Woods, H. J., Woods, P. B., Nature 185, 157 (1960). (70) Parrish, W., Acta Cryst. 13, 838 (1960). (71) Pysons, J., Baker, W. T., Baker, I - -
G., X-Ray Diffraction Powder Data and Index for the Steroids.” Henry Ford Hospital, Detroit, Mich., 1958. “ (72) Pearson, W. B., “Handbook of Lattice Spacings ?,nd Structures of Metals and Alloys, Press, _ . Pergamon London, 1958. (73) Peiser, H. S., Rooksby, N. P., Wilson, A. J. C., eds., “X-Ray Diffraction of Polvcrvstalline Materials.” rev. ed.. ReLhold, New York, 1960. (74) Pepinsky, R., J. A p p l . Phys. 18, 601 (1947). (75) Pepinsky, R., Robertson, J. M.,
Speakman, J. C., eds., “Computing Methods and the Phase Problem in X-Ray Crystal Structure Analysis,” Pergamon Press, London, 1961. (76) Perutz, M. F., Rossmann, M. G., Cullis, A. F., Muirhead, H., Will, G., North, A. C. T., Nature 185,416 (1960). (77) Post. B.. Fankuchen., I.., ANAL.CHEX ‘ 28, 591‘(1956). (78) Robertson, J. M., et al., Proc. Chem. SOC.(London) 1960. 78. 82. 278;‘ 1961, 63, 75, 115, 223, 306, 331, 416. (79) Ruland, W., Acta Cryst. 12, 679 (1959).
(80) Shaffer, P. J., Jr., Schomaker, Verner, Pauling, Linus, J . Chem. Phys. 14, 648 (1946).
(81) Shirane, G., Jona, F., Pepinsky, R., Proc. I.R.E. 43, 1738 (1955). (82) Simpson, W. S., Woods, H. J., Nature 185, 157 (1960). (83) Sociktk franqaise de Min6ralogie et Cristallographie, 1 Rue Victor Cousin, France, “Index Of Crysta11o-
graphic Supplies”; also available from Wm. Parrish, I. U. Cr. Commission on Crystallographic Apparatus, Philips
Laboratories, Irvington-on-Hudson, N. Y. (84) Soviet Physics, Crystallography, translation of KristallograJiya by American InstituteOf xew (85) raphy, TayFrjRiley, New‘‘X-Ray York, 1961. (86) Taylor, H. F. J . A p p l . Chem. London 10, 317 (1960). (87) Trueblood, K. M., Phys. T o d a y 14, 45 (1961).
*.,
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(88) Wade, F. A,, Matton, R. B., “Elements of Crystallography and Miner-
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(89) Wheatley, P. J., “Determination of Molecular Structure,” Oxford Univ. Press, Oxford, 1959. Woolfson, p\I. hI., Methods in X-Ray Crystallography,” Oxford Univ. Press, Oxford, 1961.
Magnetic Susceptibility Quite often the editors receive suggestions concerning subjects which have not been covered or not covered regularly in our annual reviews. In some cases there are subjects in which work being done i s too limited to warrant regular reviews; in other cases the field or technique may be one which has not generally been considered to be analytical in nature but which has a potential for analytical applications. Magnetic susceptibility, or magnetochemistry as it is also called, i s one example. The editors are pleased, therefore, to present a review on this topic prepared b y L. N. Mulay, who has done much work in the analytical applications of magnetic susceptibility.
Review of Fundamental Developments in Analysis
Instrumentation and Some Analytical Applications of Magnetic Susceptibility I , N. Mulay, Deparfmenf o f Chemistry, University of Cincinnafi, Cincinnati 2 I , Ohio
A
of magnetism to a study of chemical problems are numerous and have been developed since the days of Faraday. However, the term magnetochemistry appears to have been introduced for the first time in 1935 by Bhatnagar and Mathur in India, who wrote the rather extensive “Physical Principles and Applications of Magnetochemistry.” I n spite of the age and usefulness of magnetism, a study of its applications to chemical problems seems to have been restricted to certain specific schools. This may be attributed in part to a lack of commercial availability of instruments for measuring magnetic susceptibility of chemical compounds under a variety of experimental conditions. Fortunately, with the advent of the techniques of nuclear magnetic resonance, the interest in magnetochemistry within and outside these schools has been revived. Considering this renewed interest, a presentation of a review in this area, written from the standpoint of analytical chemists, appears to be in order. This being the first review of its type, an attempt will be made to point out especially the salient features and trends PPLICATIOSS
in instrumentation and to indicate some analytical applications of magnetic susceptibility. References are included which go back earlier than our usual reviews; this should not, hoR-ever, be regarded as a comprehensive review on magnetochemistry itself. NOMENCLATURE AND THEORY
It is not possible to summarize within the available space the meaning of the vast number of terms used in magnetochemistry and to outline its theories. The reader is, therefore, referred to many excellent texts listed in the next section. The most important magnetic parameters on which a discussion of this review rests are the volume and specific magnetic susceptibilities and the magnetic moments. The first may be defined as the ratio of the intensity of magnetic field induced inside a unit volume of a substance to that of the applied field. The specific or mass susceptibility x is obtained by dividing the volume susceptibility K b y the density. The magnetic moment, from a physical point of view, may be defined
as the turning effect which a magnetic dipole, arising from the “spin” and “orbital” motions of electron(s), experiences when placed in a unit magnetic field. Considering the recent advances in our knowledge of the magnetic susceptibilities and moments of nuclei of elements, it has become necessary to distinguish between these and the properties ascribed to electrons. Thus the term “electronic susceptibility” often refers to the magnetic susceptibility of electrons; it corresponds to the static or bulk magnetic susceptibility x and is related to the magnetic moment g. This term should not be confused with electrical susceptibility which is related to the electric dipole moment. It may also be pointed out that a new term “ferrimagnetism” to indicate ferromagnetism arising from atoms in two kinds of sites has been introduced by Ye61 (120). This has no relationship to antiferromagnetism or to the valence state nomenclature such as ferro(cyanide) and ferri(cyanide). It may be surmised that as yet no satisfactory theory has been developed for ferromagnetism and antiferromagnetism. Indeed the work of N e d (120) VOL. 34, NO. 5, APRIL 1962
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